To know the difficulties to be encountered is always a step towards their alleviation; and these are sufficiently apparent throughout the little volume before us. They are, _First_, _inelastic air_--which cannot transmit its pulses to the ear. _Second_, strata and amorphous volumes, of unequal densities, which transmit the _air-pulses_ with unequal force; so that they produce _distinct sounds_ and _indefinite murmurs_ at equal distances from the initial pulse. _Third_, _reflecting surfaces_--the floor, the ceiling, walls, columns, and furniture of the _auditorium_; which variously reflect the waves caused by air-pulses, and produce effects analogous to the eddies and whirlpools made by conflicting currents of running water. The _first_ and _second_ of these difficulties are clearly within the province of “heat and ventilation;” and any means by which a constant tidal flow--_not a current_--of wholesome air, _from floor to ceiling_, may be produced, and by which the _un_wholesome, inelastic, heavier _gases_ generated in crowded assemblies shall be prevented from accumulating but be _forced_ to give place to the purer air, will practically solve the problem which they present. The _third_ difficulty is purely architectural. While _surfaces_ reflect what are called _pulses of sound_, and so multiply their effects, they also create conflicting waves, which partially neutralize each other, or else strike the ear in irregular succession, to destroy the unity and harmony of sound. We cannot have buildings free from the _inconveniences_ of walls, floors, and ceilings; but we can regulate and utilize surfaces to give aid in the transmission of _air-pulses_ in _one direction_, and greatly diminish the reflecting power of those that would give back conflicting waves of air. A sounding-board or arch, whose lower surface should be a semi-paraboloid, so placed that a line drawn from its highest points, and parallel to its axis, would pierce the opposite wall four feet above the floor, while the axis itself should attain the same height at a distance of forty feet from the _focus_, would be an example of what we mean by utilizing surfaces to transmit air-pulses _in one direction_. The employment of an inelastic substance, like coarse _felt_, between the _furring_ of a wall and the _lathing_, would undoubtedly tend to destroy its ability to reflect the “_pulse of sound_.” And hollow cast-iron columns, _filled with clay_, would hardly _vibrate_ from a pulse of air.